If $U$ is uniformly distributed with mean $5$ and variance $3$, what is $P(U<4)$












-1












$begingroup$


I'm stuck on this question, can someone help me, many thanks.



If $U$ is uniformly distributed with mean $5$ and variance $3$, what is $P(U<4)$?



update(this problem has been solved):
I made a mistake when calculating, the result should be under the condition : x ranges from a to b. The final result is 1/3.










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  • 2




    $begingroup$
    uniformly distributed over what set?
    $endgroup$
    – mathworker21
    Jan 17 at 12:44






  • 1




    $begingroup$
    Where did you get stuck with solving this? What have you tried already? Questions without context and visible effort often get downvoted and closed.
    $endgroup$
    – postmortes
    Jan 17 at 12:58
















-1












$begingroup$


I'm stuck on this question, can someone help me, many thanks.



If $U$ is uniformly distributed with mean $5$ and variance $3$, what is $P(U<4)$?



update(this problem has been solved):
I made a mistake when calculating, the result should be under the condition : x ranges from a to b. The final result is 1/3.










share|cite|improve this question











$endgroup$








  • 2




    $begingroup$
    uniformly distributed over what set?
    $endgroup$
    – mathworker21
    Jan 17 at 12:44






  • 1




    $begingroup$
    Where did you get stuck with solving this? What have you tried already? Questions without context and visible effort often get downvoted and closed.
    $endgroup$
    – postmortes
    Jan 17 at 12:58














-1












-1








-1





$begingroup$


I'm stuck on this question, can someone help me, many thanks.



If $U$ is uniformly distributed with mean $5$ and variance $3$, what is $P(U<4)$?



update(this problem has been solved):
I made a mistake when calculating, the result should be under the condition : x ranges from a to b. The final result is 1/3.










share|cite|improve this question











$endgroup$




I'm stuck on this question, can someone help me, many thanks.



If $U$ is uniformly distributed with mean $5$ and variance $3$, what is $P(U<4)$?



update(this problem has been solved):
I made a mistake when calculating, the result should be under the condition : x ranges from a to b. The final result is 1/3.







probability statistics uniform-distribution






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jan 19 at 12:50







wawawa

















asked Jan 17 at 12:42









wawawawawawa

33




33








  • 2




    $begingroup$
    uniformly distributed over what set?
    $endgroup$
    – mathworker21
    Jan 17 at 12:44






  • 1




    $begingroup$
    Where did you get stuck with solving this? What have you tried already? Questions without context and visible effort often get downvoted and closed.
    $endgroup$
    – postmortes
    Jan 17 at 12:58














  • 2




    $begingroup$
    uniformly distributed over what set?
    $endgroup$
    – mathworker21
    Jan 17 at 12:44






  • 1




    $begingroup$
    Where did you get stuck with solving this? What have you tried already? Questions without context and visible effort often get downvoted and closed.
    $endgroup$
    – postmortes
    Jan 17 at 12:58








2




2




$begingroup$
uniformly distributed over what set?
$endgroup$
– mathworker21
Jan 17 at 12:44




$begingroup$
uniformly distributed over what set?
$endgroup$
– mathworker21
Jan 17 at 12:44




1




1




$begingroup$
Where did you get stuck with solving this? What have you tried already? Questions without context and visible effort often get downvoted and closed.
$endgroup$
– postmortes
Jan 17 at 12:58




$begingroup$
Where did you get stuck with solving this? What have you tried already? Questions without context and visible effort often get downvoted and closed.
$endgroup$
– postmortes
Jan 17 at 12:58










2 Answers
2






active

oldest

votes


















2












$begingroup$

Hint:- Let us suppose $U$ follows Uniform distribution with parameter $a$ and $b$.



Mean=$E(U)=frac{b+a}{2}=5$ and Variance $=V(U)=frac{(b-a)^2}{12}=3$.






share|cite|improve this answer









$endgroup$









  • 1




    $begingroup$
    You are assuming that $U$ is continuous Uniform. All that is stated is that it is Uniform (which might be continuous or discrete)
    $endgroup$
    – wolfies
    Jan 17 at 12:47












  • $begingroup$
    Yes I know this formula, the result is 1/3 right? I just realized I made a mistake, x should be in the range from a to b
    $endgroup$
    – wawawa
    Jan 17 at 12:48










  • $begingroup$
    @ Cecilia Yes, you are correct. I forgot to mention one thing that you solve the two equations under the restriction that $a<b$.
    $endgroup$
    – user440191
    Jan 17 at 12:50










  • $begingroup$
    @ wolfies you are absolutely right. I should have mentioned that I am assuming continuous uniform distribution. However, if one assume that it is the case of discrete uniform, I think thee will be a issue regarding the consideration of the set over which it is uniformly distributed ( as mentioned by @mathworker above)
    $endgroup$
    – user440191
    Jan 17 at 12:58










  • $begingroup$
    I urge @Cecilia to consider the discrete case when the set is ${1,2,dots N}$ and see what happens.
    $endgroup$
    – user440191
    Jan 17 at 12:59





















0












$begingroup$

As the mean is directly in the middle between $a$ and $b$ you can set





  • $a = 5-x$ and $b=5+x$ for $x>0$


Now solve
$$sigma^2 = frac{(b-a)^2}{12}= frac{(2x)^2}{12}=frac{x^2}{3} = 3stackrel{x>0}{Rightarrow} x= 3$$
So, $U$ "lives" on $[a,b]=[2,8]$. It follows
$$P(U<4) = frac{4-2}{8-2}=frac{2}{6}=frac{1}{3}$$






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Thank you so much for the answer, however @Bhargob answers the question before you haha and I've already chosen his answer, thanks for your time and I really appreciated it.
    $endgroup$
    – wawawa
    Jan 17 at 14:59












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2 Answers
2






active

oldest

votes








2 Answers
2






active

oldest

votes









active

oldest

votes






active

oldest

votes









2












$begingroup$

Hint:- Let us suppose $U$ follows Uniform distribution with parameter $a$ and $b$.



Mean=$E(U)=frac{b+a}{2}=5$ and Variance $=V(U)=frac{(b-a)^2}{12}=3$.






share|cite|improve this answer









$endgroup$









  • 1




    $begingroup$
    You are assuming that $U$ is continuous Uniform. All that is stated is that it is Uniform (which might be continuous or discrete)
    $endgroup$
    – wolfies
    Jan 17 at 12:47












  • $begingroup$
    Yes I know this formula, the result is 1/3 right? I just realized I made a mistake, x should be in the range from a to b
    $endgroup$
    – wawawa
    Jan 17 at 12:48










  • $begingroup$
    @ Cecilia Yes, you are correct. I forgot to mention one thing that you solve the two equations under the restriction that $a<b$.
    $endgroup$
    – user440191
    Jan 17 at 12:50










  • $begingroup$
    @ wolfies you are absolutely right. I should have mentioned that I am assuming continuous uniform distribution. However, if one assume that it is the case of discrete uniform, I think thee will be a issue regarding the consideration of the set over which it is uniformly distributed ( as mentioned by @mathworker above)
    $endgroup$
    – user440191
    Jan 17 at 12:58










  • $begingroup$
    I urge @Cecilia to consider the discrete case when the set is ${1,2,dots N}$ and see what happens.
    $endgroup$
    – user440191
    Jan 17 at 12:59


















2












$begingroup$

Hint:- Let us suppose $U$ follows Uniform distribution with parameter $a$ and $b$.



Mean=$E(U)=frac{b+a}{2}=5$ and Variance $=V(U)=frac{(b-a)^2}{12}=3$.






share|cite|improve this answer









$endgroup$









  • 1




    $begingroup$
    You are assuming that $U$ is continuous Uniform. All that is stated is that it is Uniform (which might be continuous or discrete)
    $endgroup$
    – wolfies
    Jan 17 at 12:47












  • $begingroup$
    Yes I know this formula, the result is 1/3 right? I just realized I made a mistake, x should be in the range from a to b
    $endgroup$
    – wawawa
    Jan 17 at 12:48










  • $begingroup$
    @ Cecilia Yes, you are correct. I forgot to mention one thing that you solve the two equations under the restriction that $a<b$.
    $endgroup$
    – user440191
    Jan 17 at 12:50










  • $begingroup$
    @ wolfies you are absolutely right. I should have mentioned that I am assuming continuous uniform distribution. However, if one assume that it is the case of discrete uniform, I think thee will be a issue regarding the consideration of the set over which it is uniformly distributed ( as mentioned by @mathworker above)
    $endgroup$
    – user440191
    Jan 17 at 12:58










  • $begingroup$
    I urge @Cecilia to consider the discrete case when the set is ${1,2,dots N}$ and see what happens.
    $endgroup$
    – user440191
    Jan 17 at 12:59
















2












2








2





$begingroup$

Hint:- Let us suppose $U$ follows Uniform distribution with parameter $a$ and $b$.



Mean=$E(U)=frac{b+a}{2}=5$ and Variance $=V(U)=frac{(b-a)^2}{12}=3$.






share|cite|improve this answer









$endgroup$



Hint:- Let us suppose $U$ follows Uniform distribution with parameter $a$ and $b$.



Mean=$E(U)=frac{b+a}{2}=5$ and Variance $=V(U)=frac{(b-a)^2}{12}=3$.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Jan 17 at 12:45







user440191















  • 1




    $begingroup$
    You are assuming that $U$ is continuous Uniform. All that is stated is that it is Uniform (which might be continuous or discrete)
    $endgroup$
    – wolfies
    Jan 17 at 12:47












  • $begingroup$
    Yes I know this formula, the result is 1/3 right? I just realized I made a mistake, x should be in the range from a to b
    $endgroup$
    – wawawa
    Jan 17 at 12:48










  • $begingroup$
    @ Cecilia Yes, you are correct. I forgot to mention one thing that you solve the two equations under the restriction that $a<b$.
    $endgroup$
    – user440191
    Jan 17 at 12:50










  • $begingroup$
    @ wolfies you are absolutely right. I should have mentioned that I am assuming continuous uniform distribution. However, if one assume that it is the case of discrete uniform, I think thee will be a issue regarding the consideration of the set over which it is uniformly distributed ( as mentioned by @mathworker above)
    $endgroup$
    – user440191
    Jan 17 at 12:58










  • $begingroup$
    I urge @Cecilia to consider the discrete case when the set is ${1,2,dots N}$ and see what happens.
    $endgroup$
    – user440191
    Jan 17 at 12:59
















  • 1




    $begingroup$
    You are assuming that $U$ is continuous Uniform. All that is stated is that it is Uniform (which might be continuous or discrete)
    $endgroup$
    – wolfies
    Jan 17 at 12:47












  • $begingroup$
    Yes I know this formula, the result is 1/3 right? I just realized I made a mistake, x should be in the range from a to b
    $endgroup$
    – wawawa
    Jan 17 at 12:48










  • $begingroup$
    @ Cecilia Yes, you are correct. I forgot to mention one thing that you solve the two equations under the restriction that $a<b$.
    $endgroup$
    – user440191
    Jan 17 at 12:50










  • $begingroup$
    @ wolfies you are absolutely right. I should have mentioned that I am assuming continuous uniform distribution. However, if one assume that it is the case of discrete uniform, I think thee will be a issue regarding the consideration of the set over which it is uniformly distributed ( as mentioned by @mathworker above)
    $endgroup$
    – user440191
    Jan 17 at 12:58










  • $begingroup$
    I urge @Cecilia to consider the discrete case when the set is ${1,2,dots N}$ and see what happens.
    $endgroup$
    – user440191
    Jan 17 at 12:59










1




1




$begingroup$
You are assuming that $U$ is continuous Uniform. All that is stated is that it is Uniform (which might be continuous or discrete)
$endgroup$
– wolfies
Jan 17 at 12:47






$begingroup$
You are assuming that $U$ is continuous Uniform. All that is stated is that it is Uniform (which might be continuous or discrete)
$endgroup$
– wolfies
Jan 17 at 12:47














$begingroup$
Yes I know this formula, the result is 1/3 right? I just realized I made a mistake, x should be in the range from a to b
$endgroup$
– wawawa
Jan 17 at 12:48




$begingroup$
Yes I know this formula, the result is 1/3 right? I just realized I made a mistake, x should be in the range from a to b
$endgroup$
– wawawa
Jan 17 at 12:48












$begingroup$
@ Cecilia Yes, you are correct. I forgot to mention one thing that you solve the two equations under the restriction that $a<b$.
$endgroup$
– user440191
Jan 17 at 12:50




$begingroup$
@ Cecilia Yes, you are correct. I forgot to mention one thing that you solve the two equations under the restriction that $a<b$.
$endgroup$
– user440191
Jan 17 at 12:50












$begingroup$
@ wolfies you are absolutely right. I should have mentioned that I am assuming continuous uniform distribution. However, if one assume that it is the case of discrete uniform, I think thee will be a issue regarding the consideration of the set over which it is uniformly distributed ( as mentioned by @mathworker above)
$endgroup$
– user440191
Jan 17 at 12:58




$begingroup$
@ wolfies you are absolutely right. I should have mentioned that I am assuming continuous uniform distribution. However, if one assume that it is the case of discrete uniform, I think thee will be a issue regarding the consideration of the set over which it is uniformly distributed ( as mentioned by @mathworker above)
$endgroup$
– user440191
Jan 17 at 12:58












$begingroup$
I urge @Cecilia to consider the discrete case when the set is ${1,2,dots N}$ and see what happens.
$endgroup$
– user440191
Jan 17 at 12:59






$begingroup$
I urge @Cecilia to consider the discrete case when the set is ${1,2,dots N}$ and see what happens.
$endgroup$
– user440191
Jan 17 at 12:59













0












$begingroup$

As the mean is directly in the middle between $a$ and $b$ you can set





  • $a = 5-x$ and $b=5+x$ for $x>0$


Now solve
$$sigma^2 = frac{(b-a)^2}{12}= frac{(2x)^2}{12}=frac{x^2}{3} = 3stackrel{x>0}{Rightarrow} x= 3$$
So, $U$ "lives" on $[a,b]=[2,8]$. It follows
$$P(U<4) = frac{4-2}{8-2}=frac{2}{6}=frac{1}{3}$$






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Thank you so much for the answer, however @Bhargob answers the question before you haha and I've already chosen his answer, thanks for your time and I really appreciated it.
    $endgroup$
    – wawawa
    Jan 17 at 14:59
















0












$begingroup$

As the mean is directly in the middle between $a$ and $b$ you can set





  • $a = 5-x$ and $b=5+x$ for $x>0$


Now solve
$$sigma^2 = frac{(b-a)^2}{12}= frac{(2x)^2}{12}=frac{x^2}{3} = 3stackrel{x>0}{Rightarrow} x= 3$$
So, $U$ "lives" on $[a,b]=[2,8]$. It follows
$$P(U<4) = frac{4-2}{8-2}=frac{2}{6}=frac{1}{3}$$






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Thank you so much for the answer, however @Bhargob answers the question before you haha and I've already chosen his answer, thanks for your time and I really appreciated it.
    $endgroup$
    – wawawa
    Jan 17 at 14:59














0












0








0





$begingroup$

As the mean is directly in the middle between $a$ and $b$ you can set





  • $a = 5-x$ and $b=5+x$ for $x>0$


Now solve
$$sigma^2 = frac{(b-a)^2}{12}= frac{(2x)^2}{12}=frac{x^2}{3} = 3stackrel{x>0}{Rightarrow} x= 3$$
So, $U$ "lives" on $[a,b]=[2,8]$. It follows
$$P(U<4) = frac{4-2}{8-2}=frac{2}{6}=frac{1}{3}$$






share|cite|improve this answer









$endgroup$



As the mean is directly in the middle between $a$ and $b$ you can set





  • $a = 5-x$ and $b=5+x$ for $x>0$


Now solve
$$sigma^2 = frac{(b-a)^2}{12}= frac{(2x)^2}{12}=frac{x^2}{3} = 3stackrel{x>0}{Rightarrow} x= 3$$
So, $U$ "lives" on $[a,b]=[2,8]$. It follows
$$P(U<4) = frac{4-2}{8-2}=frac{2}{6}=frac{1}{3}$$







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Jan 17 at 12:58









trancelocationtrancelocation

14.1k1829




14.1k1829












  • $begingroup$
    Thank you so much for the answer, however @Bhargob answers the question before you haha and I've already chosen his answer, thanks for your time and I really appreciated it.
    $endgroup$
    – wawawa
    Jan 17 at 14:59


















  • $begingroup$
    Thank you so much for the answer, however @Bhargob answers the question before you haha and I've already chosen his answer, thanks for your time and I really appreciated it.
    $endgroup$
    – wawawa
    Jan 17 at 14:59
















$begingroup$
Thank you so much for the answer, however @Bhargob answers the question before you haha and I've already chosen his answer, thanks for your time and I really appreciated it.
$endgroup$
– wawawa
Jan 17 at 14:59




$begingroup$
Thank you so much for the answer, however @Bhargob answers the question before you haha and I've already chosen his answer, thanks for your time and I really appreciated it.
$endgroup$
– wawawa
Jan 17 at 14:59


















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